Are shorthanded goals momentum killers?

Check out this post on the new version of Rink Stats.

Shorthanded goals are powerplay killers. You hear this all the time when you watch hockey games. But how true is this conventional wisdom? It certainly doesn't seem very common for a team to concede a shorthanded goal and then quickly follow it with a powerplay goal of their own. But it's also true that a majority of powerplays don't result in a goal, regardless of whether a SHG was conceded or not.

The question of how much SHGs kill a team's momentum on the powerplay is one that I've always thought about. Below, I take a first crack at answering the question. I show that having a SHG scored against you lowers your probability of scoring a PPG by about 10 percentage points. And early shorthanded goals have a bigger effect on a team's powerplay momentum that late ones.

The graph below shows the probability of a team scoring a powerplay goal, given that a certain number of seconds in the powerplay have already passed without a PPG. The red line shows this probability for all 5 on 4 powerplays in which no shorthanded goal had been scored up until that time (or perhaps was never scored). The blue line indicates the probability of getting a powerplay goal, given that a shorthanded goal had already been scored at an earlier time in the PP.

It's important for me to note that I'm only looking at penalties that were called during a 5 on 5, and resulted in only one player being put in the box for two minutes. I tried to be more comprehensive by looking at all powerplays (including 5 on 3s, and 4 on 3s), but doing so was unbelievably frustrating, to say the least. I also throw out any powerplays or goals that occurred when one of the goals was empty. This left about 40,000 powerplays to analyze over the past 6 NHL regular seasons.

What stands out from this graph is that it appears that shorthanded goals that come early in the penalty seem to adversely affect the full strength team's probability of capitalizing on the powerplay opportunity. I say this because the blue line is below the red one for about the first 45 seconds. After that time, the blue line runs above the red one, although both have a similar downward trajectory until the end of the 2 minutes of powerplay.

Because of the relatively low number of SHGs (only a few hundred), the blue line is pretty choppy. In the rest of the post I'll use some more sophisticated statistical methods to smooth out the relationship and more concretely answer the question of whether giving up a SHG makes a team less likely to score a PPG.

First I used logistic regression to look for a difference in the goal scoring rate between penalties that featured a SHG and penalties that did not. Logistic regression models the (natural log of the) odds of whether a particular event occurred. In this case, the event I'm modeling (my dependent variable) is whether or not each powerplay resulted in a powerplay goal. The explanatory (independent variable) of interest is whether or not there was a shorthanded goal scored during the penalty. The table below shows the results from this regression.

	Coefficient	Standard error
Intercept	-1.66668*	0.01399
Was there a SHG?	-1.08237*	0.15792

The results in the table indicate that there was a statistically significant correlation between SHGs and PPGs, and that correlation is in the direction we'd expect. That's to say, having a shorthanded goal during a penalty significantly diminishes the probability of a powerplay goal being scored during that penalty.

The coefficients in the table are not incredibly informative, even to a trained eye. To deal with that, I used Monte Carlo simulations to transform the results into a more meaningful metric. The regression indicates that 5 on 4 penalties that do not feature a SHG result in a PPG about 15.88% of the time (with a 95% confidence interval of [.1552, .1625]). In contrast when a SHG is scored, the team on the powerplay only converts about 6.11% of the time (with a confidence interval of [0.0449, 0.7981]). This 9 to 10 percentage point gap seems to really suggest that SHGs really do kill powerplay momentum.

But this regression doesn't take into account the information of when the shorthanded goal came during the powerplay. It could be the case that early shorthanded goals may have a different effect on a team's chances of scoring a PPG than late ones.

To account for this possibility I estimated 115 different logistic regressions. All of these were set up in a similar fashion to the one described above. The only difference is that the dataset used for each regression had data points dropped if there had already been a powerplay goal scored by that point in the penalty time. In other words, the 60^th regression I estimated included only penalties in which a PPG was not scored in the first 60 seconds. I only did 115 regressions (instead of 120) because the regression results from the final 5 seconds suffered from what is called colinearity (akin a divide-by-zero problem, matrix algebra-style).

The results from these 115 regressions are shown in the graph below. Each line represents the decrease in the probability of scoring a PPG when a SHG had already been scored (similar to the 9% or 10% decrease described above).

What's clear, and pretty fascinating to me, is that the momentum-killing effect of a SHG only seems to apply when the shorty is scored early in the penalty. The lines in red indicate that when I subset the data to include only penalties in which a PPG had not yet been scored, the regression results are statistically significant. The black lines indicate correlations that are not statistically significant, so I have little certainty saying that SHGs affect the probability of a PPG for those cases.

The key takeaway from the graph is that a SHG that is scored, say, 20 seconds into the powerplay diminishes the chance of a PPG by about 10 percentage points, on average. A SHG that is scored 90 seconds into the powerplay has almost a zero effect on the probability of a PPG. The reason for this probably accounted for by the fact that a team that the longer a powerplay goes on, the lower the probability of a PPG occurring, regardless of whether there's a SHG or not. Put another way, the probability of scoring a PPG in the last 10 or 20 seconds of the penalty is really low, for cases both with and without a prior SHG. Because these probabilities are low, it doesn't seem that SHGs make you less likely to score a PPG.

So what has this told us about the effect of shorthanded goals on powerplay success? On average, having a SHG against decreases your chance of converting on the powerplay by about 10 percentage points. This effect is biggest effect comes when the SHG comes early. So if you're going to give up a SHG, do it late. Or just don't give one up at all. Or score your powerplay goal really early and don't give the other team a chance to kill your momentum by getting a shorty of their own.